This self-study had two purposes. First, the authors were interested to examine their own beliefs and belief structures, including how these beliefs influenced their instructional practices. Second, the authors were interested to explore possible commonalities across their personal findings that could be identified as fundamental beliefs for all mathematics teacher educators that in turn might serve as tools for others’ growth. The authors identified four common fundamental beliefs about mathematics teacher education which they shared and which were instrumental in further examination of their own beliefs and practices: (1) mathematics is problematic and generated through sense-making; (2) a community of learners enhances learning; (3) mathematics teacher educators need to be explicitly aware of the learner in different contexts; and (4) teaching is complex at all levels.

In this article, the authors have designed a new assessment instrument in order to evaluate the effectiveness of an experimental elementary mathematics field experience course. The findings suggest that prediction assessments effectively evaluate the pedagogical content knowledge that authors are seeking to foster among the prospective teachers.

The article describes a year long study on professional development, for elementary teachers. The teaching experiment involved close mathematical interactions with a pair of students after school, in the context of solving fractions tasks. The authors anticipated that each teacher would have more opportunity to develop insight into students’ mathematics.